Molecular Dynamics Simulations of Mutilayer Films of Polyelectrolytes and Nanoparticles

Transcription

1 Langmuir 2006, 22, Molecular Dynamics Simulations of Mutilayer Films of Polyelectrolytes and Nanoparticles Junhwan Jeon,, Venkateswarlu Panchagnula,, Jessica Pan, and Andrey V. Dobrynin*,,# Polymer Program, Institute of Materials Science, Department of Chemistry, and Department of Physics, UniVersity of Connecticut, Storrs, Connecticut 06269, and Department of Chemical Engineering, Columbia UniVersity, New York, New York ReceiVed December 20, In Final Form: March 6, 2006 We performed molecular dynamics simulations of multilayer assemblies of flexible polyelectrolytes and nanoparticles. The film was constructed by sequential adsorption of oppositely charged polymers and nanoparticles in layer-by-layer fashion from dilute solutions. We have studied multilayer films assembled from oppositely charged polyelectrolytes, oppositely charged nanoparticles, and mixed films containing both nanoparticles and polyelectrolytes. For all studied systems, the multilayer assembly proceeds through surface overcharging after completion of each deposition step. There is almost linear growth in the surface coverage and film thickness. The multilayer films assembled from nanoparticles show better layer stratification but at the same time have higher film roughness than those assembled from flexible polyelectrolytes. 1. Introduction The layer-by-layer deposition of charged molecules, in which a substrate is sequentially exposed to solutions of oppositely charged macromolecules, is a new and promising technique for fabrication of layered polymeric nanocomposites. 1-8 This technique is now routinely used for fabrication of ultrathin films from synthetic polyelectrolytes, DNA, proteins, charged nanoparticles (e.g., metallic, semiconducting, magnetic, ferroelectric materials), nanoplatelets, and other supramolecular species. The multilayered thin films and coatings have potential applications in drug delivery, catalysis, functional responsive coatings for controlling release and adhesion, biosensors and bioreactors, photonic devices such as light emitting diodes, biocompatibility, and separation membranes (see, for review, refs 5, 6, 8, and 9). The structure of multilayered films depends on the rigidity of the building blocks. For example, flexible polyelectrolytes in two component multilayers are not stratified into well-defined layers but are interdiffused over several adjoining layers showing significant intermixing. 1,10-16 The name fuzzy multilayers was coined for such systems. Interpenetration between neighboring * Corresponding author. avd@ims.uconn.edu. Polymer Program, Institute of Materials Science, University of Connecticut. Present address: Department of Chemical Engineering, Vanderbilt University. Department of Chemistry, University of Connecticut. Present address: PerkinElmer Life and Analytical Sciences, 549 Albany St., Boston, MA Department of Chemical Engineering, Columbia University. # Department of Physics, University of Connecticut. (1) Decher, G. Science 1997, 277, (2) Decher, G. In The polymeric materials encyclopedia: synthesis, properties and applications; Slasmone, J. C., Ed.; CRC Press: Boca Raton, FL, (3) Decher, G.; Eckle, M.; Schmitt, J.; Struth, B. Curr. Opin. Colloid Interface Sci. 1998, 3, (4) Hammond, P. T. Curr. Opin. Colloid Interface Sci. 1999, 6, (5) Sukhishvili, S. A. Curr. Opin. Colloid Interface Sci. 2005, 10, (6) Schonhoff, M. Curr. Opin. Colloid Interface Sci. 2003, 8, (7) Schonhoff, M. J. Phys. Condens. Matter 2003, 15, R1781-R1808. (8) Decher, G.; Schlenoff, J. B., Eds. Multilayer Thin Films: Sequential Assembly of Nanocomposite Materials; Wiley-VCH: New York, (9) Sukhorukov, G. B.; Fery, A.; Mohwald, H. Prog. Polym. Sci. 2005, 30, (10) Decher, G.; Lvov, Y.; Schmitt, J. Thin Solid Films 1994, 244, (11) Kellogg, G. J.; Mayes, A. M.; Stockton, W. B.; Ferreira, M.; Rubner, M. F.; Satija, S. K. Langmuir 1996, 12, layers can be reduced by using more rigid blocks for multilayer assembly. This was shown for multilayers containing rigid inorganic platelets and nanoparticles Molecular simulations of multilayer formation provide useful information about multilayer assembly processes and factors governing the film buildup. Monte Carlo simulations of multilayer film assemblies from mixtures of oppositely charged polyelectrolytes near charged spherical particles, charged cylinders, and uniformly charged surface were performed by Messina et al These papers tested the hypothesis that multilayering is an equilibrium process, which occurs not only when one proceeds in a stepwise fashion, as done in experiments, 1-8 but also when oppositely charged polyelectrolytes are added together and the (12) Korneev, D.; Lvov, Y.; Decher, G.; Schmitt, J.; Yaradaikin, S. Physica B 1995, 213, (13) Losche, M.; Schmitt, J.; Decher, G.; Bouwman, W. G.; Kjaer, K. Macromolecules 1998, 31, (14) Lvov, Y.; Decher, G.; Haas. H.; Mohwald, H.; Kalachev, A. Physica B 1994, 198, (15) Decher, G. In Multilayer Thin Films: Sequential Assembly of Nanocomposite Materials; Decher, G., Schlenoff, J. B., Eds.; Wiley-VCH: New York, (16) Schlenoff, J. B. In Multilayer Thin Films: Sequential Assembly of Nanocomposite Materials; Decher, G., Schlenoff, J. B., Eds.; Wiley-VCH: New York, (17) Kleinfeld, E. R.; Ferguson, G. S. Science 1994, 265, (18) Glinel, K.; Laschewsky, A.; Jonas, A. M. Macromolecules 2001, 34, (19) Lvov, Y.; Ariga, K.; Ichinose, I.; Kunitake, T. Langmuir 1996, 12, (20) Schmitt, J.; Decher, G.; Dressick, W. J.; Brandow, S. L.; Geer, R. E.; Shashidhar, R.; Calvert, J. M. AdV. Mater. 1997, 9, (21) Joly, S.; Kane, R.; Radzilowski, L.; Wang, T.; Wu, A.; Cohen, R. E.; Thomas, E. L.; Rubner, M. F. Langmuir 2000, 16, (22) Koetse, M.; Laschewsky, A.; Verbiest, T. Mater. Sci. Eng, C 1999, 10, (23) Lvov, Y.; Ariga, K.; Onda, M.; Ichinose, I.; Kunitake, T. Langmuir 1997, 13, (24) Ariga, K.; Lvov, Y.; Kunitake, T. J. Am. Chem. Soc. 1997, 119, (25) Ariga, K.; Lvov, Y.; Onda, M.; Ichinose, I.; Kunitake, T. Chem. Lett. 1997, 26, (26) Kotov, N. A. In Multilayer Thin Films: Sequential Assembly of Nanocomposite Materials; Decher, G., Schlenoff, J. B., Eds.; Wiley-VCH: New York, (27) Messina, R. Langmuir 2003, 19, (28) Messina, R. J. Chem. Phys. 2003, 119, (29) Messina, R.; Holm, C.; Kremer, K. J. Polym. Sci., Part B 2004, 42, (30) Messina, R. Macromolecules 2004, 37, /la053444n CCC: $ American Chemical Society Published on Web 04/08/2006

2 4630 Langmuir, Vol. 22, No. 10, 2006 Jeon et al. resulting solution is exposed to a charged substrate. It was shown that additional short-range attractive interactions between polyelectrolytes and the surface are necessary to successfully initiate chain adsorption. These simulations do not represent the experimental situation in which polyelectrolytes are deposited from a solution in a sequential manner. 1-8 Thus, it was impossible to test the linear increase of the layer thickness and mass with the number of deposition steps as seen in the experiments. The molecular dynamics simulations were also recently used to study the sequential deposition of polyelectrolyte chains at a charged surface 31,32 and at charged spherical particles. 33,34 In these simulations the charged substrates were periodically exposed to dilute polyelectrolyte solutions. The steady-state film growth proceeds through a charge reversal of the adsorbed polymeric film, which leads to an increase in the polymer surface coverage and in the average layer thickness after completion of the first few deposition steps. In the case of adsorption onto a charged spherical particle, the polymer adsorbed amount grows faster than linear with number of deposition steps. This unusual behavior is due to the increase in the polymer adsorbing area after completion of the each deposition step. In the case of multilayer deposition at charged surfaces, MD simulations have shown that the film build up follows a linear growth with both the thickness of the adsorbed layer and polymer surface coverage increasing linearly with the number of deposition steps. 31 This steady state linear growth regime is generally observed in experiments after the deposition of the first few layers. 1-8 For partially charged chains with a fraction of charged monomers f ) 1/2 and 1/3, the growth rate of the polymer surface coverage is higher than in the case of fully charged chains. In the case of partially charged chains, there are an additional 1/f - 1 monomers added to the adsorbed layer for each adsorbed charge. This is in agreement with experimental observations of the thicker layers for partially charged polyelectrolytes compared to very thin layers obtained for the fully charged chains. Unfortunately, all previous molecular simulations were dealing with multilayers assembled from linear polyelectrolytes. In this paper, we use MD simulations to study the effect of the molecular rigidity on the layer-by-layer assembly. We perform MD simulations of the multilayered films formed from flexible polyelectrolytes, polyelectrolytes and nanoparticles, and oppositely charged nanoparticles. Our simulation results show that incorporation of the nanoparticles into multilayered films results in a better layer separation in comparison with that in the films formed by flexible polyelectrolyte chains. However, this layered structure comes with the price of a higher film roughness. The rest of the manuscript is organized as follows. The model and simulation details are described in section 2. In section 3, we present simulation results with a detailed discussion of the evolution of the surface coverage and film thickness, polymer density profile, film roughness, and surface overcharging during the deposition process. Finally, in section 4, we summarize our results. 2. Model and Simulation Details The molecular dynamics simulations of multilayer assemblies were performed from dilute solutions of linear polyelectrolytes and charged nanoparticles. The flexible polyelectrolytes were (31) Patel, P. A.; Jeon, J.; Mather, P. T.; Dobrynin, A. V. Langmuir 2005, 21, (32) Abu-Sharkh, B. J. Chem. Phys. 2005, 123, (33) Panchagnula, V.; Jeon, J.; Dobrynin, A. V. Phys. ReV. Lett. 2004, 93, (34) Panchagnula, V.; Jeon, J.; Rusling, J. F.; Dobrynin, A. V. Langmuir 2005, 21, Figure 1. C32 fullerene-like structure of nanoparticle with bond length equal to σ. modeled by chains of charged Lennard-Jones (LJ) particles (beads) with a diameter of σ and a degree of polymerization of N ) 32. The charged nanoparticles consisted of 32 charged beads and have a diameter equal to 4σ. To model charged nanoparticles, we utilized the fullerene C32 structure by rescaling the coordinates of the C atoms in such a way to set the bond length between them to σ (see Figure 1). The simulation box had the following dimensions L x L y L z ) 40σ 41.6σ 81σ. The adsorbing positively charged surface located at z ) 0 was modeled by a hexagonally packed lattice of N surface ) 1920 particles with a diameter of σ. Every second bead on the surface had a univalent charge. A similar but uncharged nonselective surface is located in the opposite side of the simulation box, z ) 81σ, to prevent macromolecules from escaping and hence maintaining 2-D periodicity in the lateral (x and y) directions. All particles in the system interacted through the truncated-shifted Lennard-Jones (LJ) potential U LJ (r ij ) ) {4ɛ LJ [( σ r ij ) 12 - ( σ r ij ) 6 - ( σ r cut ) 12 + ( σ r cut ) 6 ] r e r cut 0 r > r cut (1) where r ij is the distance between ith and jth beads and σ is the bead diameter chosen to be the same regardless of the bead type. The cutoff distance, r cut ) 2.5σ, was chosen for surfacenanoparticle/polymer and nanoparticle/polymer pairs, and r cut ) 6 2σ was chosen for other pairwise interactions. The interaction parameter ɛ LJ is equal to k B T for all pairs, where k B is the Boltzmann constant, and T is the absolute temperature. The choice of parameters for surface-nanoparticle/polymer and nanoparticle/ polymer LJ-potential corresponds to effective short-range attraction while interaction potential with r cut ) 6 2σ corresponds to pure repulsive interactions. The connectivity of beads in both nanoparticles and polyelectrolyte chains was maintained by the finite extension nonlinear elastic (FENE) potential (2) U FENE (r) )- 1 2 k spring R 2 max ln( 1 - r2 R max 2) with the spring constant k spring ) 30k B T/σ 2, where R max ) 1.5σ is the maximum bond length. The combination of FENE and LJ potentials prevents the bonds from crossing each other during the simulation run.

3 Mutilayer Films of Polyelectrolytes and Nanoparticles Langmuir, Vol. 22, No. 10, system NN NP PP PN Table 1. Procedure of the Layer-by-Layer Deposition and System Notations procedure of the layer-by-layer deposition nanoparticles(-) f nanoparticles(+) f nanoparticles(-) ff nanoparticles(-) f polyelectrolytes(+) f nanoparticles(-) ff polyelectrolytes(-) f polyelectrolytes(+) f polyelectrolytes(-) ff polyelectrolytes(-) f nanoparticles(+) f polyelectrolytes(-) ff The rigidity of the nanoparticles was kept by the harmonic bending potential U bend (θ) ) 1 2 k bend (θ - θ 0 )2 (3) where θ is an angle between two consecutive bonds and the bending constant being k bend ) 100k B T/rad 2. The value of the valence angle θ 0 was equal to 108 for pentagons and to 120 for hexagons (see Figure 1). Interaction between any two charged beads with charge valences q i and q j, and separated by a distance r ij, is given by the Coulomb potential U Coul (r ij ) ) k B T l B q i q j r ij (4) where l B ) e 2 /ɛk B T is the Bjerrum length, defined as the length scale at which the Coulomb interaction between two elementary charges e, in a dielectric medium with the dielectric constant ɛ, is equal to the thermal energy k B T. In our simulations, the value of the Bjerrum length l B is equal to σ. Counterions from charged surface, polyelectrolyte chains or nanoparticles are explicitly included in our simulations. The particle-particle particle-mesh (PPPM) method 35,36 for the slab-geometry, with the correction term 37 implemented in LAMMPS 38 with the sixth order charge interpolation scheme and estimated accuracy 10-5, was used for calculations of the electrostatic interactions. In this method, the 2-D periodic images of the system are periodically replicated along the z direction with distance L ) 3L z between their boundaries. Simulations are carried out in a constant number of particles, volume, and temperature ensemble (NVT) with periodic boundary conditions in the x and y directions. The constant temperature is achieved by coupling the system to a Langevin thermostat. 35 In this case, the equation of motion of ith particle is m dvb i dt (t) ) FB i - ξvb i + FB R i (t) (5) where Vb i is the bead velocity, and FB i is the net deterministic force acting on ith bead of mass m. FB i R is the stochastic force with zero average value FB i R (t) ) 0 and δ-functional correlations FB i R (t)fb i R (t ) ) 6ξk B Tδ(t - t ). The friction coefficient ξ is set to ξ ) m/τ LJ, where τ LJ is the standard LJ time τ LJ ) σ(m/ɛ LJ ) 1/2. The velocity-verlet algorithm with a time step t ) 0.01τ LJ is used for integration of the equations of motion (eq 5). Simulations of the multilayer assembly are performed by alternating a substrate exposure to dilute solutions of nanoparticles or polyelectrolytes in four different ways as explained in Table 1. The simulation procedure of the multilayer assembly by sequential deposition of charged macromolecules is similar to (35) Frenkel, D.; Smit, B. Understanding Molecular Simulations; Academic Press: San Diego, CA, (36) Dobrynin, A. V. In Simulation methods for polymers; Kotelyanskii, M., Theodorou, D. N., Eds.; Marcel Dekker: New York, (37) Yeh, I.; Berkowitz, M. L. J. Chem. Phys. 1999, 111, (38) Plimpton, S. LAMMPS User s Manual, Sandia National Lab.: Albuquerque, NM, 2005 that previously implemented in refs 31, 33, and 34. At the beginning of the first deposition step, counterions from the charged surface are uniformly distributed over the simulation box. Negatively charged polyelectrolytes or nanoparticles (M 1 ) 160) consisting of 32 monomers each, corresponding to monomer concentration c ) 0.038σ -3, together with their counterions were then added to the simulation box, and the simulation continues until the completion of 10 6 MD steps. After completion of the first simulation run ( dipping step), unadsorbed polyelectrolyte chains were removed ( rinsing step). The unadsorbed polyelectrolytes or nanoparticles were separated from the adsorbed ones by using a cluster algorithm with a cutoff radius equal to 2.5σ. 31,33,34 (The large cutoff distance was selected to ensure the correct identification of the adsorbed nanoparticles.) The cluster analysis was performed by analyzing the matrix of distances between all beads in the system. After completion of the simulation run (deposition step), only the counterions needed for compensation of the excess charge of the growing film were kept in the simulation box to maintain electroneutrality of the system. At the beginning of the second deposition step, the simulation box is refilled with M 2 ) M 1 ) 160 oppositely charged polyelectrolytes or nanoparticles together with their counterions resulting in the concentration of newly added polyelectrolytes/ nanoparticles being the same as before, c ) 0.038σ -3. This is followed by the simulation run ( dipping step ) lasting another 10 6 MD steps. The duration of each simulation run was sufficient for the system to reach steady state. (The optimization of the duration of the simulation run was discussed in our previous publication. 31 ) We repeated the dipping and rinsing steps to model 10 deposition steps. During each deposition step, the data were collected during the final MD steps. In the case of the nanoparticles-nanoparticles system, we have increased the simulation box size along z direction by the average increment of the layer thickness z after each deposition step, starting with the third deposition step. This allowed us to maintain approximately the same volume accessible to nanoparticles on top of the growing film during the whole deposition process. Such increase in the simulation box size is not necessary for other systems since the growing film occupies the smaller fraction of the simulation box in comparison with NN system. 3. Results and Discussion The evolution of the film structure during deposition steps from 1 to 5 is shown in Figure 2. Nanoparticles and polyelectrolytes deposited during different deposition steps are displayed in different colors. The counterions are not shown in the snapshots. Oppositely charged nanoparticles/flexible polyelectrolytes were alternately adsorbed on the charged substrate in a series of consecutive deposition steps. The construction of the multilayered film can start either with deposition of nanoparticles (NN and NP systems) or with deposition of flexible polyelectrolytes (PP and PN systems). The structure of the adsorbed layer appearing after completion of the first deposition step is qualitatively different for nanoparticle and flexible polyelectrolyte systems. The nanoparticles, forming the primer layer at the substrate (NP and NN systems), are arranged into an almost perfect hexagonal lattice. Such a high degree of ordering in the distribution of

4 4632 Langmuir, Vol. 22, No. 10, 2006 Jeon et al. Figure 2. Evolution of the multilayer assembly at charged surface. Snapshots are taken after completion of the deposition steps 1-5. The positively charged particles on the substrate are shown in green and neutral particles are colored in black. The molecules deposited during different deposition steps are colored as follows: blue (1), red (2), cyan (3), magenta (4), and orange (5). nanoparticles is due to strong electrostatic repulsion between them. On the contrary, the flexible polyelectrolytes (PP and PN systems) cover the surface uniformly forming a thin polymeric layer. Deposition of the positively charged species during the second deposition step (in our simulations, the surface is positively charged) alters the well-organized structure of the surface layer. For all systems, positively charged chains or nanoparticles form a complex with previously adsorbed ones exposing the original substrate. The amount of the uncovered space is the largest for the NN and PN systems. Thus, the screening of the strong electrostatic interactions between negatively charged nanoparticles can be effectively achieved either by covering nanoparticles with polyelectrolytes (one polyelectrolyte chain can form a complex with several nanoparticles) or by forming strings of negatively and positively charged nanoparticles with positively charged nanoparticles filling the gaps between negatively charged ones. The deposition of positively charged nanoparticles on top of the negatively charged polyelectrolytes (PN system) leads to a lesser amount of the uncovered original substrate. In this case, the positively charged particles are positioned on top of the regions with the higher polymer surface coverage. One can envision this process as nanoparticles pulling polyelectrolyte chains to protect themselves from unfavorable electrostatic repulsion with a positively charged substrate. Deposition of the positively charged polyelectrolytes on top of the negatively charged chains leads to nucleation of several small holes protruding toward the bare substrate. As the simulation run continues, these small holes coagulate forming one huge hole shown in Figure 2. The coalescence of the smaller holes is a result of minimization of the line tension energy, which favors the appearance of the single hole. As the film buildup proceeds further, the newly adsorbing Figure 3. Number of molecules in contact with the substrate as a function of the number of deposition steps. Filled circles, open circles, filled triangles, open triangles correspond to nanoparticlesnanoparticles, nanoparticles-polymers, polymers-polymers, and polymers-nanoparticles systems, respectively. macromolecules first cover the substrate and then start building up the new layer on top of the previously assembled ones. For NP and NN systems, the gaps and empty spots on the substrate persist as the number of deposition steps increases. This ultimately leads to a hollow thicker film in comparison with the film started with the deposition of flexible polyelectrolytes.

5 Mutilayer Films of Polyelectrolytes and Nanoparticles Langmuir, Vol. 22, No. 10, Figure 4. Surface topography as obtained from the bead height distribution after completion of the fifth deposition step for the nanoparticlesnanoparticles (a), nanoparticles-polymers (b), polymers-polymers (c), and polymers-nanoparticles (d) systems. The reorganization of the film structure can be followed by monitoring the number of molecules in contact with the original substrate N contact (see Figure 3). In every odd deposition step, negatively charged molecules adsorb onto the surface resulting in an increase of the number of contacts, N contact. At the same deposition step, nanoparticles (NN and NP systems) are in contact with the surface to a lesser extent than the flexible polyelectrolytes (PP and PN systems). For flexible polyelectrolytes, it is sufficient to displace a chain segment to free a space for newly incoming chains to contact a substrate and still keep a chain in contact with the substrate. The number of nanoparticles in contact with the surface is limited by their large excluded volume and electrostatic repulsion between them. After completion of the second deposition step in the NP system, nanoparticles are pulled together (neutralized) by polyelectrolytes (see Figure 2) leaving an empty space available for the additional adsorption of new nanoparticles directly on the substrate. This available space is filled by newly adsorbed nanoparticles during the third deposition step (see Figure 3). Consequently, the number of nanoparticles in contact with the substrate in NP system is larger than in NN system. Similarly the number of polyelectrolytes in contact with the surface in the PP system is larger than in the PN system. Therefore, the observed jump in the number of molecules in contact with the substrate at every other deposition step, as seen in Figure 3, is a result of the reorganization process within growing film. Another fact that has to be pointed out here is the rigidity of the molecules adsorbed at the even deposition steps. Nanoparticles adsorbed at the even deposition steps have a larger excluded volume, as compared to the flexible polyelectrolytes, which prevents chains from approaching the surface at the odd deposition steps. For the NN system, the number of nanoparticles in the contact with the surface saturates after completion of the fifth deposition step. The number of chains in contact with the substrate for the PP system also shows saturation, but this happens at the later stage (after completion of the 8th deposition step) indicating high mobility and flexibility in the local chain rearrangements in comparison with that for the nanoparticles. However, for PN and NP systems, the number of molecules in contact with the substrate continues to increase during the entire simulation run, 10 deposition steps. This is due to high porosity and heterogeneity inside growing films. There is the following order in the number of molecules in contact with the substrate PP > PN > NP > NN. The surface roughness shows a strong correlation with the type of molecules covering the substrate (primer layer) as well as with the rigidity of macromolecules used for the film assembly. To obtain the film topography, we utilize the bead height sorting algorithm which selects a bead located at the furthest distance from the substrate for each bin in the array that covers the surface. The 3-D plot of this matrix gives a local film height distribution that provides information similar to the atomic force microscopy (AFM) measurements. All of the topographic images shown in Figure 4 are obtain using the last configurations of the fifth deposition step simulations. The snapshots of these configurations are shown in the last column in Figure 2. Several steps can be clearly identified based on the color assigned to the local film thickness. The NN system has

6 4634 Langmuir, Vol. 22, No. 10, 2006 Jeon et al. Figure 6. Surface coverage Γ, the number of adsorbed beads per unit area, as function of the number of deposition steps. Notations are the same as in Figure 3. Figure 5. Dependence of the average film thickness (a) and the surface roughness (b) on the number of deposition steps. Notations are the same as in Figure 3. four steps, NP and PN systems have three steps, and the PP system has a smooth surface coverage if an insignificant bump is ignored. Based on this observation, one can see that the surface becomes rougher when nanoparticles are used in the film assembly (NN > NP g PN > PP). The average thickness of the layer h is calculated as the average value of the height distribution and the surface roughness is obtained from the second moment of this distribution R rh ) N -1 bin i [(h i - h ) 2 ] 1/2 where N bin is the number of bins. These quantities were averaged during the last MD steps during each deposition step. Figure 5 shows the evolution of the average film thickness h and film roughness with the number of deposition steps. The film thickness increases almost linearly with the number of deposition steps for the systems containing flexible chains. The incorporation of the nanoparticles results in a faster increase in the average film thickness. This should not be surprising since nanoparticles have a larger excluded volume and leave less space available for the newly adsorbed molecules. The fastest growing film thickness is observed for the NN system. However, this fast increase in the film thickness leads to higher film roughness (see Figure 5b). Although the surface roughness for the systems containing nanoparticles steadily increases with the number of deposition steps, it saturates for the film consisting of flexible polyelectrolytes (PP system) after completion of four deposition steps. Table 2. Number of Adsorbed Molecules after Each Deposition Step deposition system step NN NP PP PN deposition system step NN NP PP PN The increase in the surface coverage Γ, the number of adsorbed beads per unit area, during the film build up process is shown in Figure 6. The number of macromolecules adsorbed during each deposition step is given in Table 2. The steady state regime is achieved after completion of the first couple of deposition steps, after which the surface coverage increases linearly with number of deposition steps for the systems containing polyelectrolyte chains. The surface coverage shows slightly faster than linear increase for the NN system. Such nonlinear increase in the surface coverage is an indication that the growth in the film mass not only occurs from the surface but also has a bulk Figure 7. Overcharging fraction ( Q /Q ads ) as a function of the number of deposition steps. Notations are the same as in Figure 3.

7 Mutilayer Films of Polyelectrolytes and Nanoparticles Langmuir, Vol. 22, No. 10, Figure 8. Density profiles of beads belonging to fully charged polyelectrolyte chains and nanoparticles after completion of 10 deposition steps obtained for multilayer films consisting of nanoparticles-nanoparticles (a), nanoparticles-polymers (b), polymers-polymers (c), and polymers-nanoparticles (d). component. This can happen for a highly heterogeneous film with a lot of hollow space. A rough surface provides nanoparticles/ polyelectrolytes with more surface area to contact with than a smooth surface does. This effect is already observed for the second deposition step simulations where a larger amount of macromolecules could adsorb on the substrate covered by nanoparticles in comparison with that for surface covered by polyelectrolytes. This initial roughness difference determines the order of the adsorption amount beyond the fourth deposition step leading to the following sequence of the growth in the film mass NN > NP > PN > PP. The overcharging process during the steady-state film growth is shown in Figure 7, where the ratio of the absolute value of the layer overcharging, Q, excess of the positively or negatively charged monomer including those belonging to the substrate within growing polymer film to the net charge carried by adsorbed chains at a given deposition step, Q ads ) (N(s) - N(s - 1)) (where N(s) is the total number of adsorbed beads after completion of the sth step), is plotted versus the number of deposition steps. This quantity appears to fluctuate around 0.5 for all studied systems. This observation can be explained as follows. For a steady state growth, half of the adsorbed molecules are used for neutralization of the film excess charge, whereas the other half recreates the film charge necessary for the adsorption of the next layer. If this ratio is smaller than 0.5, the film eventually stops growing. However, if it exceeds 0.5, the surface coverage will show exponential growth. In both cases, the growth process is unstable. Thus, the surface overcharging plays a dual role: it rebuilds the surface properties for the next deposition layer and prevents the unrestricted growth of the adsorbed amount, which is stabilized by the electrostatic repulsions between the excess charges. The fluctuations in the overcharging fraction Q /Q ads around a value of 0.5 are due to the fluctuations in the number of adsorbed molecules and the substrate effect. Increasing the system size could diminish the first contribution. This is indeed the case if one compares the results shown in Figure 7 for the PP system with our previous simulations results. The system size used in this simulation is twice the size of the systems studied in ref 31. The substrate effect is more pronounced for the NP and PN systems, which show gradual decrease in fluctuations of overcharging fraction Q /Q ads with the number of deposition steps. For these systems, the substrate still influences the film growth pattern up to the tenth deposition step. It is interesting to point out that the overcharging fraction Q /Q ads is always larger than 0.5 after completion of the deposition of polyelectrolyte chains and it is below 0.5 after deposition of nanoparticles. This trend in evolution of the overcharging fraction is a reflection of the higher flexibility of the polyelectrolyte chains that are capable of wrapping around nanoparticles and at the same time better fit into the available empty space. In the PN system, the number of polyelectrolytes adsorbed at each deposition step is always larger than or equal to that of nanoparticles adsorbed at the immediately preceding deposition step. The intermixing between molecules adsorbed during different deposition steps is shown in Figure 8, which displays the density distribution F n (z) of beads belonging to the molecules adsorbed

8 4636 Langmuir, Vol. 22, No. 10, 2006 Jeon et al. Figure 9. Film composition, F(z) )F - (z) -F + (z), of multilayer films consisting of nanoparticles-nanoparticles (a), nanoparticlespolymers (b), polymers-polymers (c), and polymers-nanoparticles (d). during different deposition steps. These distribution functions were averaged separately for each set of molecules adsorbed at different deposition steps during the final simulation run representing the 10th deposition step. This procedure enables us to see how well adsorbed molecules intermix within layered films. For example, nanoparticles adsorbed during the first deposition step never move and stay in contact with the surface during the entire simulation run (see Figure 8, parts a and b). This happens due to the strong electrostatic attraction between the substrate and oppositely charged nanoparticles. Nevertheless, there is continuous rearrangement of nanoparticles within the growing film. For example, nanoparticles adsorbed during the third deposition step could come in contact with the substrate. The bead density profile for these nanoparticles has two peaks. The first peak corresponds to nanoparticles in contact with the substrate, whereas another one is due to nanoparticles forming the third layer. Similar distribution exists for nanoparticles adsorbed during the fourth deposition step. A fraction of these particles completes formation of the second layer, and the remaining part initiate formation of the fourth layer (see Figure 8a). As the film thickness grows, the peaks in the bead density distribution functions become less pronounced indicating the weakening of the effect of the substrate rigidity on the film structure. The more pronounced molecule rearrangements are seen for the systems containing flexible polyelectrolytes. In these systems, polyelectrolytes adsorbed during the first deposition step (see Figure 8, parts c and d) could span through the entire film thickness showing significant intermixing (interdiffusion) between polyelectrolyte chains deposited during different deposition steps. The film composition, characterized by the difference in local density of beads belonging to negatively and positively charged molecules, F(z) )F - (z) -F + (z), is shown in Figure 9. This function, F(z), clearly indicates a multilayer structure of the assembled films. Comparing the most probable location of the center of mass of nanoparticles shown by arrows, we can see an almost perfect layered distribution of nanoparticles within multilayers (see Figure 9, parts a, b, and d). It is worthwhile to note that because nanoparticles are rigid they are impenetrable and typical layer thickness is comparable with the nanoparticles diameter. This also means that a better stratification of molecules within the multilayer film can be achieved by using more rigid building blocks. On the contrary, the flexible polyelectrolytes in two component films intermix over several adjacent layers. Despite strong intermixing in the systems containing flexible polyelectrolytes, a multilayered nature of the film still persists. This can be clearly seen in Figure 9b-d which shows the existence of alternating layers with excesses of positively or negatively charged molecules. The film composition, shown in Figure 9, supports the threezone structure of the multilayer film. Zone I contains the layer in the vicinity from the adsorbing surface with an excess of

9 Mutilayer Films of Polyelectrolytes and Nanoparticles Langmuir, Vol. 22, No. 10, molecules carrying a charge opposite to that on the substrate. The thickness of this layer depends on the molecular rigidity. For example, for the films consisting of the flexible polyelectrolytes or for the film with nanoparticles in which the primer layer is formed by flexible polyelectrolytes, the thickness of this zone is on the order of the couple bead sizes. However, for films assembled from nanoparticles or for mixed films with nanoparticles forming the primer layer, the thickness of this zone is of the order of the nanoparticle size. Zone II contains complexes of oppositely charged molecules. In the case of flexible polyelectrolytes and mixed films containing both flexible chains and nanoparticles, the molecules are well intermixed and exhibit 1:1 charge stoichiometry. Zone III includes the outmost layer along with counterions, which neutralizes the excess charge in zone III. The growth of the film occurs by increasing the thickness of the zone II with newly adsorbed molecules, displacing counterions and overcharging the external molecular layer. 4. Conclusions In conclusion, we have performed molecular dynamics simulations of layer-by-layer assemblies of polyelectrolytes and nanoparticles from dilute solutions. In the case of the multilayers formed by flexible polyelectrolytes, the polyelectrolytes are not perfectly stratified within the multilayer film. There is strong intermixing between chains deposited during different deposition steps. However, despite the high degree of intermixing between chains, there are almost perfect oscillations in film composition. For multilayer films consisting of nanoparticles, there is better stratification of the layers with almost constant thickness of the layer composed of nanoparticles. For all studied systems, the process of multilayer formation occurs over several successive deposition steps. Usually, four deposition steps are required to complete formation of the two layers. The initial deposition steps cover the surface partially and in the subsequent steps, any unfilled portions are occupied eventually leading to a more uniform coverage, regardless of the initial layer. The film thickness and surface coverage increase almost linearly with the number of deposition steps, indicating the steady-state film growth. The multilayer films formed by nanoparticles have a higher roughness than films consisting of flexible polymers. Acknowledgment. The authors are grateful to the National Science Foundation for the financial support under grants DMR and DMR LA053444N